Theorem equncomi 3273

Description: Inference form of equncom 3272. (Contributed by Alan Sare, 18-Feb-2012.)

Hypothesis

Ref	Expression
equncomi.1	|- A = ( B u. C )

Assertion

Ref	Expression
equncomi	|- A = ( C u. B )

Proof of Theorem equncomi

Step	Hyp	Ref	Expression
1		equncomi.1	. 2 |- A = ( B u. C )
2		equncom 3272	. 2 |- ( A = ( B u. C ) <-> A = ( C u. B ) )
3	1, 2	mpbi 144	1 |- A = ( C u. B )

Syntax hints:   = wceq 1348   u. cun 3119

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125

This theorem is referenced by:  disjssun  3478  difprsn1  3719  unidmrn  5143  phplem1  6830  djucomen  7193